On conjugacy of maximal abelian subalgebras and the outer automorphism group of the Cuntz algebra

被引：8

作者：

Conti, Roberto ^{[1
]}

Hong, Jeong Hee ^{[2
]}

Szymanski, Wojciech ^{[3
]}

机构：

[1] Univ Roma La Sapienza, Sez Matemat, Dipartimento Sci Base & Applicate Ingn, I-00161 Rome, Italy

[2] Korea Maritime & Ocean Univ, Dept Data Informat, Busan 606791, South Korea

[3] Univ Southern Denmark, Dept Math & Comp Sci, DK-5230 Odense M, Denmark

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2015年 / 145卷 / 02期

基金：

新加坡国家研究基金会;

关键词：

ROHLIN PROPERTY; WEYL GROUP; ENDOMORPHISMS; SHIFTS;

D O I：

10.1017/S0308210513001364

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of maximal abelian subalgebras in O-n. In particular, we exhibit an uncountable family of maximal abelian subalgebras, conjugate to the standard maximal abelian subalgebra D-n via Bogolubov automorphisms, that are not inner conjugate to D-n.

引用

页码：269 / 279

页数：11

共 27 条

[1]

Beggs E. J., 2002, ACAD SCI PARIS SER I, V24, P26

[2] Homogeneity of the pure state space of the Cuntz algebra [J].

Bratteli, O ;

Kishimoto, A .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 171 (02) :331-345

[3]

CONNES A, 1977, ACTA SCI MATH, V39, P39

[4]

CONNES A, 1975, ANN SCI ECOLE NORM S, V8, P383

[5]

Connes A., 1973, Ann. Sci. Ecole Norm. Sup., V6, P133

[6] Remarks on the index of endomorphisms of Cuntz algebras [J].

Conti, R ;

Pinzari, C .

JOURNAL OF FUNCTIONAL ANALYSIS, 1996, 142 (02) :369-405

[7]

Conti R., 2012, THETA SERIES ADV MAT, P1

[8] The Weyl group of the Cuntz algebra [J].

Conti, Roberto ;

Hong, Jeong Hee ;

Szymanski, Wojciech .

ADVANCES IN MATHEMATICS, 2012, 231 (06) :3147-3161

[9] The restricted Weyl group of the Cuntz algebra and shift endomorphisms [J].

Conti, Roberto ;

Hong, Jeong Hee ;

Szymanski, Wojciech .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 667 :177-191

[10] LABELED TREES AND LOCALIZED AUTOMORPHISMS OF THE CUNTZ ALGEBRAS [J].

Conti, Roberto ;

Szymanski, Wojciech .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (11) :5847-5870

← 1 2 3 →